73
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Strategic use of the unsayable: Paradox as argument in Gödel's theorem

Pages 80-93 | Published online: 05 Jun 2009

Notes

  • Hilbert . 1902 . Bulletin of the American Mathematical Society
  • January 1931 . Monatshefte fur Mathematik und Physik January ,
  • Gödel . 1931 . “Uber Formal Unentscheidbare Satze der Principia Mathematica und Verwandter Systeme I” ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") . Monatshefte for Mathematik und Physik, , 38 : 173 – 198 .

Works cited

  • Aristotle . 1991 . On Rhetoric: A Theory of Civic Discourse. , Edited by: Kennedy , George A. New York : Oxford UP .
  • Boyer , Carl B. 1991 . A History of Mathematics. , 2nd ed. , Edited by: Merzbach , Uta C. New York : Wiley . 1968. Rev.
  • Cherwitz , Richard A. and Darwin , Thomas J. 1995 . “Why the ‘Epistemic’ in Epistemic Rhetoric? The Paradox of Rhetoric as Performance.” . Text and Performance Quarterly , X : 189 – 205 .
  • Davis , Philip J. and Hersh , Reuben . 1987 . “Rhetoric and Mathematics.” . In The Rhetoric of the Human Sciences: Language and Argument in Scholarship and Public Affairs. , Edited by: Nelson , John S. , Megill , Allan and McCroskey , Donald N. 53 – 68 . Madison : U of Wisconsin P .
  • Dawson , John W. Jr. 1997 . Logical Dilemmas: The Life and Work of Kurt Gödel , Wellesley, MA : Peters .
  • Dawson , John W. Jr. 1986 . “Introductory Note to 1931a, 1932e, f and g.” . In Kurt Gödel: Collected Works Vol. I Publications 1929–1936. , Edited by: Feferman , Solomon . 196 – 199 . New York : Oxford UP .
  • Dawson , John W. Jr. 1988 . “The Reception of Gödel's Incompleteness Theorems.” . In Gödel's Theorem in Focus. , Edited by: Shanker , S.G. 74 – 95 . London : Croom Helm .
  • Dragalin , A.G. 1988 . “Antimony.” . In Encyclopaedea of Mathematics , Dordrecht, , Holland : Kluwer .
  • Feferman , Solomon . 1988 . “Kurt Gödel: Conviction and Caution.” . In Gödel's Theorem in Focus. , Edited by: Shanker , S.G. 1 – 16 . London : Croom Helm .
  • Fernandez , James . 1980 . “Edification by Puzzlement.” . In Explorations in African Systems of Thought. , Edited by: Karp , Ivan and Bird , Charles S. 44 – 59 . Bloomington : Indiana UP .
  • Fraenkel , Abraham A. , Bar‐Hillel , Yehoshua and Levey , Azriel . 1973 . Foundations of Set Theory. , 2nd rev. ed. , Studies in Logic and the Foundations of Mathematics 67 Amsterdam : Nooral‐Hollandsche U.M. .
  • Frege , Gottlob . 1952 . “On Sense and Reference.” . In Translations from the Philosophical Writings of Gottlob Frege. , Edited by: Black , Max , Geach , Peter and Black , Max . 56 – 78 . Oxford : Blackwell .
  • Frege , Gottlob . 1952 . “Translation of Parts of Frege's Grundgesetze der Arithmetik: Selections from Volume I.” . In Translations from the Philosophical Writings of Gottlob Frege. , Edited by: Jourdain , P.E.B. , Stachelroth , J. , Geach , Peter and Black , Max . 137 – 158 . Oxford : Blackwell .
  • Gaonkar , Dilip Parameshwar . 1997 . “The Idea of Rhetoric in the Rhetoric of Science.” . In Rhetorical Hermeneutics: Invention and Interpretation in the Age of Science. , SUNY Ser. In Speech Communication Edited by: Gross , Alan G. and Keith , William M. 25 – 85 . Albany : State U of New York .
  • Gentzen , Gerhard . 1969 . The Collected Papers of Gerhard Gentzen. , Edited by: Szabo , M.E. Amsterdam : North‐Holland .
  • Gödel , Kurt . 1986 . “Discussion on Providing a Foundation for Mathematics (1931a).” . In Kurt Gödel: Collected Works, Vol. 1. Publications 1929–1936. , Edited by: Dawson , John W. Jr. , Feferman , Solomon , Dawson , John W. Jr. , Kleene , Stephen C. , Moore , Gregory H. , Solvay , Robert M. and van Heijenoort , Jean . Vol. 1 , 201 – 203 . New York : Oxford UP .
  • Gödel , Kurt . 1986 . “Postscript.” . In Kurt Gödel: Collected Works. Vol. 1. Publications 1929–1936. , Edited by: Dawson , John W. Jr. , Feferman , Solomon , Dawson , John W. Jr. , Kleene , Stephen C. , Moore , Gregory H. , Solvay , Robert M. and Heijenoort , Jean van . Vol. 1 , 203 – 205 . New York : Oxford UP .
  • Gödel , Kurt . 1962 . On Formally Undecidable Propositions of Principia Mathematica and Related Systems , Edited by: Meltzer , B. Edinburgh : Oliver . (1931)
  • Gödel , Kurt . 1970 . “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I” (1931) ” . In Frege and Gödel: Two Fundamental Texts in Mathematical Logic. , Edited by: van Heijenoort , Jean . 83 – 108 . Cambridge : Harvard UP .
  • Guillen , Michael . 1983 . Bridges to Infinity: The Human Side of Mathematics , Los Angeles : Tarcher .
  • Helmer , Olaf . 1937 . “Perelman versus Gödel.” . Mind , 46 : 58 – 60 .
  • Heyting , Arend . 1971 . “ Introduction ” . In Intuitionism: An Introduction. , 3rd ed. , Studies in Logic and the Foundations of Mathematics Edited by: Brouwer , L.EJ. , Heyting , A. , Robinson , A. and Suppes , P. Amsterdam : North‐Holland . 1971
  • Hikins , James W. and Zagacki , Kenneth S. 1988 . “Rhetoric, Philosophy, and Objectivism: An Attenuation of the Claims of the Rhetoric of Inquiry.” . Quarterly Journal of Speech , 74 : 201 – 228 .
  • Hilbert , David . 1902 . “Mathematical Problems: Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900.” . In Bulletin of the American Mathematical Society. , 2nd Ser. 8 Edited by: Newson , Mary Winston . 437 – 479 .
  • Hofstede , Geert . 1991 . Cultures and Organizations: Software of the Mind , London : McGraw‐Hill Europe .
  • Hofstadter , Douglas R. 1979 . Gödel, Escher, Bach: An Eternal Golden Braid , New York : Vintage .
  • Kline , Morris . 1980 . Mathematics, the Loss of Certainty , New York : Oxford UP .
  • Lakatos , Imre , ed. 1967 . International Colloquium in the Philosophy of Science: Problems in the Philosophy of Mathematics , Amsterdam : North‐Holland .
  • Leff , Michael C. 1978 . “In Search of Ariadne's Thread: A Review of the Recent Literature on Rhetorical Theory.” . Central States Speech Journal , 29 : 73 – 91 .
  • Liu , James J.Y. 1988 . Language‐Paradox‐Poetics: A Chinese Perspective. , Edited by: Lynn , Richard John . Princeton : Princeton UP .
  • Lyotard , Jean‐François . 1984 . The Postmodern Condition: A Report on Knowledge. , Edited by: Bennington , Geoff and Massumi , Brian . Minneapolis : U of Minnesota P . 1979
  • Melia , Trevor . 1984 . “And Lo the Footprint . . . Selected Literature in Rhetoric and Science.” . Quarterly Journal of Speech , 70 : 303 – 312 .
  • Nagel , Ernest and Newman , James R. 1958 . Gödel's Proof , New York : New York UP .
  • Penrose , Roger . 1989 . The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics , Oxford : Oxford UP .
  • Resnik , Michael D. 1988 . “On the Philosophical Significance of Consistency Proofs.” . In Gödel's Theorem in Focus. , Edited by: Shanker , S.G. 115 – 130 . London : Croom Helm .
  • Russell , Bertrand . 1951 . The Autobiography of Bertrand Russell. , Vol. 2 , Boston : Little .
  • Russell , Bertrand . 1945 . A History of Western Philosophy: and its Connection with Political and Social Circumstances from the Earliest Times to the Present Day , New York : Simon .
  • Russell , Bertrand . 1938 . The Principles of Mathematics. , 2nd ed. , New York : Norton . 1903
  • Schrag , Calvin O. 1985 . “Rhetoric Resituated at the End of Philosophy.” . Quarterly Journal of Speech , 71 : 164 – 174 .
  • Scott , Robert L. 1990 . “Epistemic Rhetoric and Criticism: Where Barry Brummett Goes Wrong.” . Quarterly Journal of Speech , 76 : 300 – 303 .
  • Scott , Robert . 1988 . “Non‐Discipline as a Remedy for Rhetoric? A Reply to Victor Vitanza.” . Rhetoric Review , 6 : 233 – 7 .
  • Scott , Robert L. 1967 . “On Viewing Rhetoric as Epistemic.” . Central States Speech Journal , 18 : 9 – 17 .
  • Shanker , Stuart G. 1988 . “Wittgenstein's Remarks on the Significance of Gödel's Theorem.” . In Gödel's Theorem in Focus. , Edited by: Shanker , S.G. London : Croom Helm .
  • Taussky‐Todd , Olga . 1987 . “Remembrances of Kurt Gödel.” . In Gödel Remembered: Gödel‐Symposium in Salzburg 10–12 July 1983. , History of Logic IV Edited by: Weingartner , Paul and Schmetterer , Leopold . 31 – 41 . Napoli : Bibliopolis .
  • Wang , Hao . 1996 . A Logical Journey: From Gödel to Philosophy , Cambridge : MIT P .
  • Wang , Hao . 1987 . Reflections on Kurt Gödel , Cambridge : MIT P .
  • Wartofsky , Marx W. 1968 . Conceptual Foundations of Scientific Thought: An Introduction to the Philosophy of Science , London : Macmillan .
  • Weimer , Walter B. 1977 . “Science as a Rhetorical Transaction: Toward a Nonjustificational Conception of Rhetoric.” . Philosophy and Rhetoric , 10 : 1 – 29 .
  • Whitehead , Alfred North and Russell , Bertrand . 1925 . Principia Mathematica , 2nd Ed. , Cambridge : UP . 1910
  • Whitson , Steve and Poulakos , John . 1993 . “Nietzsche and the Aesthetics of Rhetoric.” . The Quarterly Journal of Speech , 79 : 131 – 145 .
  • Zermelo , Ernst . 1987 . “Letter to Mr. Reinhold Baer 10 July 1931, Freiburg.” . In Gödel Remembered: Gödel‐Symposium in Salzburg 10–12 July 1983. , History of Logic IV Edited by: Weingartner , Paul and Schmetterer , Leopold . 43 – 48 . Napoli : Bibliopolis .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.